Write the following cubes in expanded form:

$open parentheses straight x minus 2 over 3 straight y close parentheses cubed$

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Solution

open parentheses straight x minus 2 over 3 straight y close parentheses cubed equals x cubed minus open parentheses 2 over 3 y close parentheses cubed minus 3 left parenthesis x right parenthesis open parentheses 2 over 3 y close parentheses open parentheses x minus 2 over 3 y close parentheses

| Using Identity VII

equals space straight x cubed minus 8 over 27 straight y cubed minus 2 xy open parentheses straight x minus 2 over 3 straight y close parentheses equals space straight x cubed minus 8 over 27 straight y cubed minus 2 straight x squared straight y plus 4 over 3 xy squared equals space straight x cubed minus 2 straight x squared straight y plus 4 over 3 xy squared minus 8 over 27 straight y cubed.

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